After you get the Hi-Jump in Norfair, you head back to Brinstar to go to your next destination.
Brinstar
Go to the left until you reach the tall room, then go up. Use the save room if you want, then exit the save room. Keep going up until you reach the uppermost blue door. Go through.
Go to the right side of the room and shoot the red light in the metal thing to make the metal thing go up. Roll beneath it and go to the right, then use bombs in the gap in the wall. Press Jump while in Morph Ball to jump up into the tunnel. Go into the uppermost metal tube and go to the right. There is a Tangle Vine Fruit to the right, but it's immune to all your weapons. Jump up onto the ledge above, and shoot the block to the left of the metal pipe. As Morph Ball, press jump to jump into the metal tube, then roll through it. You'll fall through a Pit Block at the end. Go through the door.
You can go through the door on the right and use the save room if you wish. Then go through the left door of the save room. Shoot the ceiling slightly right of the center of the room to open a hole all the way through, then jump up through it. Press Jump to stand on top of it, but don't walk left. There are Pit Blocks that you will fall through, so you'll have to go up through the hole in the ceiling again. Instead, if there are Parasites sticking to you, use a bomb to kill them, then jump up to the left to grab the ledge there. Shoot the ceiling and jump up through the hole, then go through the door.
There are two Tangle Vine Fruits, but wait a moment and the Parasites will destroy them. Then when the Parasites stick to you, use a Bomb to destroy them. Then go to the left, jump with Morph Ball to get over the pillar, then jump and grab the pillar to the left. As you go left, hold the jump button because the blocks down below are slow Pit Blocks that will drop you into the acid if you stay on them too long. If you hold the jump button, you'll bounce off of the Pit Block before it crumbles. At the leftmost side, stop jumping and you'll fall through to the floor below.
Go to the left, but jump quickly, because these are also slow Pit Blocks. When you roll to the left in the tunnel, push left so you fall into the gap on the left. Otherwise, you'll land on another slow Pit Block. On the left side, jump and drop a bomb next to the cracked blocks. Don't bomb the Parasites if they stick to you. If they stick to you, stand as close as possible to the Tangle Vine Fruit to make the Parasites go onto it instead. When the Tangle Vine Fruit is gone, use bombs to get rid of the Parasites that stick to you, go through the gap on the left, shoot the red door with a Missile, and go through.
Shoot the egg and take the item to get the Varia Suit. This makes you immune to acid and super-heated rooms, and increases your defense against damage.
Recharge your health and weapons with the Chozo Statue, then go back through the door. Go to the right and stand on the slow Pit Block and let it drop you into the acid. You still move slowly in it, but you no longer take damage from it. Go to the right, to the lowest part of the floor, and bomb the rocky part of the floor to open a hole. Go down into the hole, bomb the left side, and keep bombing to the left to reach the Energy Tank.
Then go to the right side of the room and go through the door, then shoot the cracked blocks below you and go down through them. Go down to the bottom of the room and go through the door on the right. Use the save room, then go through the door on the right.
Go through this room and get the Missile Tank, then go to the right and fall into the acid. Use bombs to break through the blocks beneath you but don't go down below yet. Instead, jump to go through the pipe on the right. Shoot the red light on the metal thing and let the Parasites stick to you and don't bomb them. Go down through where you bombed the blocks, then go to the right and get as close as possible to the Tangle Vine Fruit to make the Parasites go onto it. When it's gone, roll through the tunnel on the right.
Go up and use the Chozo Statue to find out your next destination. Then go to the right and go through the door.
Go down to the blue door at the bottom of this area. Go through. Then go left through several rooms until you're in another tall room. Go down to the bottom and go through the door on the right. Keep going to the right to reach the elevator down to Norfair. Go down.